Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · physics/0508002

The tensor analytical relationships of Dirac's equation

Cornelius Lanczos
View original source ↗Read source document ↗Export metadata ↓

Abstract

Dirac's equation of the electron will be discussed by using quaternions as the basis of a new formalism which seems to be very well adapted to the problem. The transformation properties of the equations as well as the invariant and covariant [bilinear] constructions of Dirac's theory are developed uniformly and systematically. A method of obtaining a covariant formulation of the equations using customary tensor calculus also offers itself unequivocally if we duplicate the Dirac equations. (Editorial note: In this paper Lanczos introduces his ``fundamental equation,'' Eq. (54), from which two Dirac fields forming an isospin doublet, or two spin 1 fields of opposite parities, derive.)

Explore related subjects

physics.hist-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Cornelius Lanczos. 2005-08-10. The tensor analytical relationships of Dirac's equation. https://arxiv.org/abs/physics/0508002

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Scientific Promise

Scientists constantly face decisions about what lines of research to pursue. This Element introduces the philosophical debate about scientific pursuitworthiness. It explains how it can be rational to pursue a theory even if the theory is less well supported than its rivals, and it discusses existing philosophical frameworks for guiding pursuit decisions. The Element also develops a new perspective. Existing accounts focus predominantly on theories, while experiments are largely neglected. This is an important shortcoming. Theoretical promise depends on experimental promise, and experimental promise raises questions of its own. Drawing on the epistemology of experimentation, the Element advances an account of experimental pursuitworthiness. It is argued that such pursuitworthiness depends on experimental virtues like a clear signal and simplicity of design. Moreover, the kinds of uncertainty that constrain the assessment of scientific pursuits are examined. Finally, the Element highlights open questions in the philosophy of scientific pursuitworthiness.

physics.hist-ph↗
arXiv2026

Is Black Hole Evaporation Prediction Friendly?

Manchak and Weatherall (2018) formulate the black hole information paradox as a failure of predictability in black hole evaporation spacetimes, diagnosed by non-global hyperbolicity. I offer a strategy for resolving this paradox. I argue that failures of predictability in black hole evaporation are not well diagnosed by non-global hyperbolicity. I then consider two weakenings of global hyperbolicity: prediction and retrodiction friendliness, the failure of which could ground a new paradox. However, deidealized black hole evaporation models can be prediction and retrodiction friendly. Therefore, the information paradox cannot be based upon failures of global hyperbolicity, nor either retrodiction or prediction unfriendliness.

physics.hist-ph↗
arXiv2026

The Crab Nebula progenitor: recovering the 1054 AD supernova event as galactic Gamma-ray burst

In 1054 AD a daytime star appeared in the constellation of Taurus, for three weeks, and it was reported in various sources from Europe to China/Japan: it was one of the few documented galactic supernovae of the last two millenia. This paradigm has been established about sixty years ago, as the comprehension of the physics of supernovae progressed with enough observational data. The Gamma-ray bursts were discovered in the same period, but only in the past few years have their observations become daily and their distances have been fully understood as cosmological. After the explosion, the exponential decay of the luminosity in gamma-rays and X-rays has been followed with telescopes onboard dedicated satellites. Also the exponential decay of the afterglow's optical and radio frequencies have been observed with the largest optical and radio telescopes. Within the binary-driven hypernova framework, successful in explaining all the observed phases of the Gamma-ray bursts, the universal exponential decay can be extended to 1000 years after the burst, to account for the present values of Gamma and X-rays as well as optical and radio frequencies of the Crab Nebula. Both the daytime visibility of the burst, and the simultaneous radiation plagues appeared in Constantinople and Cairo is a strong evidence of the presence of Gamma-rays in the lower atmosphere, coming from the same source originating the Crab nebula. The association to the daytime visibility of that star and the following plague meets exactly the etymology of the word dis-aster, bad star.

physics.hist-ph↗